Limits on the Higgs boson lifetime and width from its decay
to four charged leptons
V. Khachatryan et al.* (CMS Collaboration)
(Received 23 July 2015; published 22 October 2015)
Constraints on the lifetime and width of the Higgs boson are obtained from H→ ZZ → 4l events using data recorded by the CMS experiment during the LHC run 1 with an integrated luminosity of 5.1 and 19.7 fb−1at a center-of-mass energy of 7 and 8 TeV, respectively. The measurement of the Higgs boson
lifetime is derived from its flight distance in the CMS detector with an upper bound ofτH< 1.9 × 10−13 s
at the 95% confidence level (C.L.), corresponding to a lower bound on the width ofΓH> 3.5 × 10−9MeV.
The measurement of the width is obtained from an off-shell production technique, generalized to include anomalous couplings of the Higgs boson to two electroweak bosons. From this measurement, a joint constraint is set on the Higgs boson width and a parameter fΛQ that expresses an anomalous coupling contribution as an on-shell cross-section fraction. The limit on the Higgs boson width isΓH< 46 MeV
with fΛQunconstrained andΓH< 26 MeV for fΛQ ¼ 0 at the 95% C.L. The constraint fΛQ < 3.8 × 10−3
at the 95% C.L. is obtained for the expected standard model Higgs boson width.
DOI:10.1103/PhysRevD.92.072010 PACS numbers: 14.80.Bn, 14.80.Ec
I. INTRODUCTION
The discovery of a new boson with mass of about 125 GeV by the ATLAS and CMS experiments[1–3]at the CERN LHC provides support for the standard model (SM) mechanism with a field responsible for generating the masses of elementary particles[4–9]. This new particle is believed to be a Higgs boson (H), the scalar particle appearing as an excitation of this field. The measurement of its properties, such as the lifetime, width, and structure of its couplings to the known SM particles, is of high priority to determine its nature.
The CMS and ATLAS experiments have set con-straints of ΓH < 22 MeV at 95% confidence level (C.L.)
on the H boson total width [10,11]from the ratio of off-shell to on-off-shell production. The precision on ΓH from direct on-shell measurements alone is approximately 1 GeV [12,13], which is significantly larger. The two experiments have also set constraints on the spin-parity properties and anomalous couplings of the H boson [14–18], finding its quantum numbers to be consistent with JPC¼ 0þþ but allowing small anomalous coupling contributions. No direct experimental limit on the H boson lifetime was set, and the possible presence of anomalous couplings was not considered in the con-straints on the H boson width. This paper provides these two measurements.
The measurement of the H boson lifetime in this paper is derived from its flight distance in the CMS detector[19], and the measurement of the width is obtained from the off-shell production technique, generalized to include anoma-lous couplings of the H boson to two electroweak bosons, WW and ZZ. From the latter measurement, a joint con-straint is set on the H boson width and a parameter that quantifies an anomalous coupling contribution as an on-shell cross-section fraction. The event reconstruction and analysis techniques rely on the previously published results [10,16,17,20], and their implementations are discussed in detail. Only the final state with four charged leptons is considered in this paper, but the constraints on the width could be improved by including final states with neutrinos in the off-shell production[10,11]. Indirect constraints on the H boson width and lifetime are also possible through the combination of data on H boson production and decay rates[12,21]. While such a combination tests the compat-ibility of the data with the SM H boson, it relies on stronger theoretical assumptions such as SM-like coupling ratios among the different final states.
Section II in this paper discusses the analysis methods for measuring the H boson lifetime and for relating the anomalous couplings of the H boson to the measurement of ΓH through the off-shell production technique. SectionIII
discusses the CMS detector and event simulation, and Sec.IV defines the selection criteria used in the analysis. SectionV describes the analysis observables, categoriza-tion, and any related uncertainty. SectionVI provides the constraints on the H boson lifetime, while Sec. VII provides the upper limits for both the H boson width and the anomalous coupling parameter investigated in this paper. The summary of results is provided in Sec.VIII. *Full author list given at the end of the article.
Published by the American Physical Society under the terms of the Creative Commons Attribution 3.0 License. Further distri-bution of this work must maintain attridistri-bution to the author(s) and the published article’s title, journal citation, and DOI.
II. ANALYSIS TECHNIQUES
The lifetime of each H boson candidate in its rest frame is determined in a four-lepton event as
Δt ¼mp4l
T
ðΔ~rT· ˆpTÞ; ð1Þ
where m4l is the four-lepton invariant mass, Δ~rT is the displacement vector between the decay vertex and the production vertex of the H boson in the plane transverse to the beam axis, and ˆpT and pT are respectively the unit vector and the magnitude of the H boson transverse momentum. The average Δt is inversely proportional to the total width:
hΔti ¼ τH ¼ ℏ
ΓH: ð2Þ
The distribution of the measured lifetimeΔt is used to set an upper limit on the average lifetime of the H boson, or equivalently a lower limit on its widthΓH, and it follows
the exponential distribution if known perfectly. The expected SM H boson average lifetime is τH ≈ 48 fm=c (16 × 10−8 fs) and is beyond instrumental precision. The technique summarized in Eq. (1) nonetheless allows the first direct experimental constraint onτH.
The upper bound on ΓH is set using the off-shell
production method [22–24] and follows the technique developed by CMS[10], where the gluon fusion and weak vector boson fusion (VBF) production mechanisms were considered in the analysis. The technique considers the H boson production relationship between the on-shell (105.6 < m4l< 140.6 GeV) and off-shell (220 < m4l< 1600 GeV) regions. Denoting each production mechanism with vv→ H → ZZ for H boson coupling to either strong (vv¼ gg) or weak (vv ¼ VV) vector bosons vv, the on-shell and off-on-shell yields are related by
σon-shell
vv→H→ZZ∝ μvvH and σoff-shellvv→H→ZZ∝ μvvHΓH; ð3Þ
whereμvvH is the on-shell signal strength, the ratio of the
observed and expected on-shell production cross sections for the four-lepton final state, which is denoted by either μggH for gluon fusion production or μVVH for VBF
production. The t¯tH process is driven by the H boson couplings to heavy quarks like the gluon fusion process, and the VH process by the H boson couplings to weak vector bosons like the VBF process. They are therefore parametrized with the same on-shell signal strengthsμggH
and μVVH, respectively. The effects of signal-background interference are not shown in Eq.(3)for illustration but are taken into account in the analysis.
The relationship in Eq.(3)implies variations of the vvH couplings as a function of m4l. This variation is assumed to be as in the SM in the gluon fusion process. The assumption
is valid as long as the production is dominated by the top-quark loop and no new particles contribute to this loop. Variation of the HVV couplings, either in the VBF or VH production or in the H→ ZZ decay, may depend on anomalous coupling contributions. An enhancement of the off-shell signal production is suggested with anomalous HVV couplings [10,25–27], but neither experimental studies of off-shell production nor realistic treatment of signal-background interference has been done with these anomalous couplings. We extend the methodology of the recent analysis of anomalous HVV couplings of the H boson[17] to study these couplings and introduce in the scattering amplitude an additional term that depends on the H boson invariant mass, ðqV1þ qV2Þ2:
AðHVVÞ ∝ a1− eiϕΛQðqV1þ qV2Þ 2 ðΛQÞ2 − e iϕΛ1ðq 2 V1þ q2V2Þ ðΛ1Þ2 × m2VϵV1ϵV2þ a2fð1Þμν fð2Þ;μνþ a3fð1Þμν ~fð2Þ;μν; ð4Þ where fðiÞμν¼ ϵμViqνVi− ϵνViqμVi is the field strength tensor of a gauge boson with momentum qVi and polarization vector ϵVi, ~fðiÞμν ¼12ϵμνρσfðiÞ;ρσ is the dual field strength
tensor, the superscript * designates a complex conjugate, and mV is the pole mass of a vector boson. The ai are complex coefficients, and theΛ1orΛQ may be interpreted
as the scales of beyond-the-SM (BSM) physics. The complex phase of theΛ1andΛQ terms are explicitly given
as ϕΛ1 and ϕΛQ, respectively. Equation (4) describes all anomalous contributions up to dimension five operators. In the SM, only the a1term appears at tree level in couplings to ZZ and WW, and it remains dominant after loop corrections. Constraints on the anomalous contributions from the a2, a3 andΛ1 terms to the H→ VV decay have been set by the CMS and ATLAS experiments [16–18] through on-shell H boson production.
TheΛQterm depends only on the invariant mass of the H
boson, so its contribution is not distinguishable from the SM in the on-shell region. This paper tests the ΛQ term
through the off-shell region. Equation (4) describes both ZZ and WW couplings, and it is assumed that ΛQ is the
same for both. The ratio of any loop contribution from a heavy particle in the HVV scattering amplitude to the SM tree-level a1 term would be predominantly real, and the imaginary part of the ratio would be small. If the con-tribution instead comes from an additional term to the SM Lagrangian itself, this ratio can only be real. Therefore, only real coupling ratios are tested such that cosϕΛQ¼ 1 and a1≥0, where a1¼2 and ΛQ → ∞ correspond to the
tree-level SM HVV scattering withμggH¼ μVVH¼ 1. The effective cross-section fraction due to theΛQterm, denoted
as fΛQ, allows a parametrization similar to the conven-tions of Λ1 in Ref. [17]. It is defined for the on-shell
gg→H→VV process assuming no contribution from other anomalous couplings as
fΛQ¼ m4H=Λ4Q ja1j2þ m4H=Λ4Q
: ð5Þ
The HVV couplings in Eq.(4)appear in both production and decay for the VBF and VH mechanisms while they appear only in decay for H boson production through gluon fusion. Isolating the former two production mechanisms, therefore, enhances the sensitivity to the contribution of anomalous couplings. While the previous study of the H boson width[10]employs dijet tagging only in the on-shell region, VBF jet identification is also extended to the off-shell region in this analysis with techniques from Ref.[20]. A joint constraint is obtained onΓH, fΛQ,μggH, andμVVH,
where the latter two parameters correspond to the H production strength in gluon fusion, and VBF or VH production mechanisms in the on-shell region, respectively.
III. THE CMS EXPERIMENT AND SIMULATION The CMS detector, described in detail in Ref. [19], provides excellent resolution for the measurement of electron and muon momenta and impact parameters near the LHC beam interaction region. Within the supercon-ducting solenoid (3.8 T) volume of CMS, there are a silicon pixel and strip tracker, a lead tungstate crystal electromag-netic calorimeter (ECAL) and a brass and scintillator hadron calorimeter. Muons are identified in gas-ionization detectors embedded in the iron flux return placed outside the solenoid. The data samples used in this analysis are the same as those described in Refs.[10,16,17,20], correspond-ing to an integrated luminosity of 5.1 fb−1 collected in proton-proton collisions at LHC with center-of-mass energy of 7 TeV in 2011 and 19.7 fb−1 at 8 TeV in 2012. The uncertainties in the integrated luminosity meas-urement are 2.2% and 2.6% for the 2011 and 2012 data sets, respectively [28,29].
The H boson signal production through gluon fusion or in association with two fermions from either vector boson fusion or associated vector boson production may interfere with the background 4l production with the same initial and final states. The background4l production is consid-ered to be any process that does not include a contribution from the H boson signal. The on-shell Monte Carlo (MC) simulation does not require interference with the back-ground because of the relatively small H boson width[10]. The off-shell production leads to a broad m4lspectrum and is generated using the full treatment of the interference between the signal and background for each production mechanism. Therefore, different techniques and tools have been used for on-shell and off-shell simulation. The sim-ulation of the H boson signal is performed at the measured value of the H boson pole mass mH ¼ 125.6 GeV in the 4l
final state [16], and the expected SM H boson width ΓSM
H ¼ 4.15 MeV [30,31] along with several other ΓH
reference values.
The two dominant H boson production mechanisms, gluon fusion and VBF, are generated on-shell at next-to-leading order (NLO) in perturbative quantum chromody-namics (QCD) using thePOWHEG[32–34]event generator.
The decay of the H boson via H→ ZZ → 4l, including interference effects of identical leptons in the final state and nonzero lifetime of the H boson, is modeled with
JHUGen 4.8.1[35–37]. In addition, gluon fusion production
with up to two jets at NLO in QCD has been generated usingPOWHEGwith theHJJprogram[38], where theMINLO
procedure [39] is used to resum all large logarithms associated with the presence of a scale for merging the matrix element and the parton shower contributions. In all of the above cases, simulations with a wide range of masses mH up to 1000 GeV [20] for H boson on-shell signal production at NLO in QCD have been used to calibrate the behavior of associated particles in the simulation of off-shell H boson signal at leading order (LO) in QCD, which is described below. The VH and t¯tH production mecha-nisms of the H boson, which have the smallest expected cross sections, and the subsequent H boson prompt decays are simulated on-shell usingPYTHIA6.4.24[40].
Four different values of the H boson lifetime have been generated with cτH ¼ 0, 100, 500, 1000 μm for the gluon
fusion production mechanism, and these samples are reweighted to model the values of lifetime in between the generated values. The only difference between gluon fusion and the other production mechanisms relevant for the constraint on the lifetime is the H boson pTspectrum,
so reweighting as a function of pTallows the modeling of
the different production mechanisms with nonzero H boson lifetime. Following the formalism in Eq.(4)for spin-zero and including nonzero spin hypotheses,JHUGensimulations
for a variety of H boson production (gluon fusion, VBF, VH, t¯tH, q¯q) and decay (H → ZZ=Zγ=γγ→ 4l) modes
have been generated with SM and BSM couplings to validate model independence of the lifetime analysis. This simulation is detailed in Ref.[17].
The off-shell H boson signal and the interference effects with the background are included at LO in QCD for gluon fusion, VBF, and VH mechanisms, while the t¯tH produc-tion is highly suppressed at higher masses and is therefore not simulated off-shell [30,31]. On-shell and off-shell events from gluon fusion production are generated with theMCFM6.7[24,41,42]andGG2VV 3.1.5[43]MC generators
while those for the VBF and associated production with an electroweak boson V are generated with PHANTOM 1.2.3
[44]. The leptonic decay of the associated V boson is modeled with a reweighting procedure based on the branching ratios of the V boson [45], and the relatively small contribution of HH production is removed from the
PHANTOM simulation. Pure signal, pure background, and LIMITS ON THE HIGGS BOSON LIFETIME AND WIDTH… PHYSICAL REVIEW D 92, 072010 (2015)
several mixed samples with signal-background interfer-ence have been produced for the analysis of the inter-ference effects. The modeling of the anomalous couplings from Eq. (4) in the off-shell H boson production is performed by reweighting the SM-like samples. An extended MCFM library provided as part of the Matrix Element Likelihood Approach (MELA) package,[35–37], allows for both reweighting and event simulation with anomalous couplings in off-shell H production, and the analytical reweighting for the fΛQparametrization used in this analysis is identical to reweighting via the MELA package.
Figure1illustrates the simulation of the gg→ 4l process with the above technique, which includes H boson off-shell production, its background, and their interference for the five signal models with the a1 (SM), a2, a3, Λ1, and ΛQ
terms in Eq. (4). In all cases, the on-shell yield and the widthΓHare constrained to the SM expectations, and large enhancements are seen in the off-shell region. The four BSM models correspond to the effective fractions fai¼ 1 defined in Ref. [17] or Eq. (5). When the on-shell contributions of the anomalous couplings are small, can-cellation effects in the off-shell region due to their inter-ference with the a1term or with the background, as in the
case of theΛQ term, may suppress the off-shell yield for a
given ΓH. Among these four BSM models, the ΛQ term results in the largest off-shell enhancement, and only the ΛQand a1terms, and their interference between each other
and the background, are considered in the width analysis. Constraints on the a2, a3, andΛ1terms have already been measured from on-shell analyses[17,18].
In the case of the off-shell MC simulation, the QCD renormalization and factorization scales are set to the dynamic scales m4l=2 for gluon fusion and m4l for the VBFþ VH signal productions and their backgrounds. Higher-order QCD corrections for the gluon fusion signal process are known to an accuracy of next-to-next-to-leading order (NNLO) and next-to-next-to-next-to-next-to-leading loga-rithms for the total cross section[30,31], and to NNLO as a function of m4l [46]. The m4l-dependent correction factors to the LO cross section (K factors) are typically in the range of 2.0 to 2.7. Although no exact calculation exists beyond the LO for the gg→ ZZ continuum back-ground, it has been recently shown [47] that the soft collinear approximation is able to describe the back-ground cross section and the interference term at NNLO. Further calculations also show that the K factors are very similar at NLO for the signal and background[48]and at NNLO for the signal and interference terms [49]. Therefore, the same K factor is used for the signal and background [46]. Similarly, QCD and electroweak cor-rections are known to an accuracy of NNLO for the VBF and VH signal contributions [30,31,50], but no calcu-lation exists beyond the LO for the corresponding back-ground contributions. The same K factors as in signal are also assumed for the background and interference con-tributions. Uncertainties due to the limited theoretical knowledge of the background K factor have a small impact on the final results.
The background q¯q → ZZ process is simulated using
POWHEG at NLO in QCD with no interference with H
boson signal production. The NLO electroweak calcula-tions [51,52]predict negative, m4l-dependent corrections to this process for on-shell Z boson pairs and are taken into account. In addition, a two-jet inclusive MadGraph 5.1.3.30
[53]simulation is used to check jet categorization in the q¯q → ZZ process. PYTHIA is used to simulate parton
showering and hadronization for all MC signal and back-ground events. The generated MC events are subsequently processed with the CMS full detector simulation, based on
Geant4 [54], and reconstructed using the same algorithm used for the events in data.
The background from Z production with associated jets, denoted as Zþ X, comes from the production of Z and WZ bosons in association with jets as well as from t¯t production with one or two jets misidentified as an electron or a muon. The estimation of the Zþ X background in the four-lepton final state is obtained from data control regions without relying on simulation[16]. (GeV) 4 m 200 300 400 500 600 700 800 Events / 20 GeV -2 10 -1 10 1 10 2 10 3 10 SM total SM bkg. =1 Q Λ , f H SM Γ = H Γ =1 a3 , f H SM Γ = H Γ =1 a2 , f H SM Γ = H Γ =1 1 Λ , f H SM Γ = H Γ 4 → gg CMSSimulation -1 (7 TeV) (8 TeV) + 5.1 fb -1 19.7 fb
FIG. 1 (color online). The m4l distributions in the off-shell region in the simulation of the gg→ 4l process with the ΛQ
(fΛQ ¼ 1), a3 (fa3¼ 1), a2(fa2¼ 1), and Λ1 (fΛ1¼ 1) terms, as open histograms, as well as the a1 term (SM), as the filled histogram, from Eq.(4) in decreasing order of enhancement at high m4l. The on-shell signal yield and the width ΓH are
constrained to the SM expectations. In all cases, the background and its interference with different signal hypotheses are included except in the case of the pure background (dotted), which has greater off-shell yield than the SM signal-background contribu-tion due to destructive interference.
IV. EVENT SELECTION
The event reconstruction and selection requirements are the same as those in the previous measurements of the H boson properties in the H→ 4l channel [10,16,17,20]. Only small modifications are made to the lepton impact parameter requirements in the lifetime analysis to retain potential signal with a displaced four-lepton vertex.
As in previous measurements [10,16,17,20], events are triggered by requiring the presence of two leptons (elec-trons or muons) with asymmetric requirements on their pT. A triple-electron trigger is also used. Electron candidates are defined by a reconstructed charged-particle track in the tracker pointing to an energy deposition in the ECAL. A muon candidate is identified as a charged-particle track in the muon system that matches a track reconstructed in the tracker. The electron energy is measured primarily from the ECAL cluster energy, while the muon momentum and the charged-lepton impact parameters near the interaction region are measured primarily by the tracker. Electrons and muons are required to be isolated from other charged and neutral particles[16]. Electrons (muons) are reconstructed for pT> 7ð5Þ GeV within the geometrical acceptance jηj < 2.5ð2.4Þ[55,56]. Trigger and reconstruction efficien-cies for muons and electrons are found to be independent on the lifetime of the H boson, similar to other studies of long-lived particles [57,58].
Events are selected with at least four identified and isolated electrons or muons to form the four-lepton can-didate. Two Z→ lþl− candidates originating from a pair of leptons of the same flavor and opposite charge are required. Thelþl−pair with an invariant mass, m1, nearest to the nominal Z boson mass is denoted Z1and is retained if it is in the range 40 < m1< 120 GeV. A second lþl− pair, denoted Z2, is required to have an invariant mass 12 < m2< 120 GeV. If more than one Z2 candidate
satisfies all criteria, the pair of leptons with the highest scalar pT sum is chosen. The lepton pT selection is
tightened with respect to the trigger by requiring at least one lepton to have pT> 20 GeV, another one to have
pT> 10 GeV, and any oppositely charged pair of leptons
among the four selected to satisfy mll> 4 GeV regardless of flavor. A Z boson decay into a lepton pair can be accompanied by final state radiation where the radiated photon is associated to the corresponding lepton to form the Z boson candidate as Z → lþl−γ [16].
The electrons and muons that comprise the four-lepton candidate are checked for consistency with a reference vertex. In the width analysis, this comparison is done with respect to the primary vertex of each event, defined as the one passing the standard vertex requirements [59] and having the largest Pp2T of all associated charged tracks. The significance of the three-dimensional impact parameter (SIP) of each lepton, calculated from the track parameters and their uncertainties at the point of closest approach to this primary vertex, is required to be less than 4[16]. This
requirement does not allow for a displaced vertex, so in order to constrain the lifetime of the H boson, the reference of the comparison is switched to the vertex formed by the two leptons from the Z1 candidate. The SIP of the two leptons from Z1is required to be less than 4, and that of the remaining two leptons is required to be less than 5. An additional requirement χ24l=dof < 6 for the four-lepton vertex is applied to further suppress the Zþ X background. Both analyses also require the presence of the reconstructed proton-proton collision vertex in each event. The combi-nation of these requirements allows for the detection of a displaced H boson decay while keeping the selection efficiencies similar between the two criteria.
After selection, the prompt-decay backgrounds originate from the q¯q → ZZ=Zγ→ 4l and gg → ZZ=Zγ→ 4l processes together with 4l production with associated fermions, such as VBF and associated V production. These backgrounds are evaluated from simulation follow-ing Refs. [10,16]. The Zþ X background may include displaced vertices due to b-quark jets and is evaluated using the observed control samples as discussed in Ref. [16], which employs the tight-to-loose lepton misidentification method. While the misidentification rates are consistent between the two different vertex selection requirements, the overall number of selected Zþ X background events is about 15% higher when using the vertex requirements of the lifetime measurement. The number of prompt-decay signal and background events is about 2% higher with these lifetime measurement requirements.
In the width analysis, the presence of jets is used as an indication of VBF or associated production with an electroweak boson decaying hadronically, such as WH or ZH. The CMS particle-flow (PF) algorithm [60–63], which combines information from all subdetectors, is used to provide an event description in the form of reconstructed particle candidates. The PF candidates are then used to build jets and lepton isolation quantities. Jets are recon-structed using the anti-kTclustering algorithm[64]with a distance parameter of 0.5, as implemented in the FastJet
package [65,66]. Jet energy corrections are applied as a function of the jet pTandη[67]. An offset correction based
on the jet area method is applied to subtract the energy contribution not associated with the high-pTscattering such as electronic noise and pileup, the latter of which results primarily from other pp collisions in the same bunch crossing [67–69]. Jets are only considered if they have pT> 30 GeV and jηj < 4.7, and if they are separated from the lepton candidates and identified final-state radiation photons.
Within the tracker acceptance, the jets are reconstructed with the constraint that the charged particles are compatible with the primary vertex. In addition, jets arising from the primary interaction are separated using a multivariate discriminator from those reconstructed due to energy deposits associated with pileup interactions, particularly LIMITS ON THE HIGGS BOSON LIFETIME AND WIDTH… PHYSICAL REVIEW D 92, 072010 (2015)
those from neutral particles not associated with the primary vertex of the event. The discrimination is based on the differences in the jet shapes, the relative multiplicity of charged and neutral components, and the fraction of pT carried by the hardest components [70]. In the width analysis, the events are split into two categories: those with two or more selected jets (dijet category) and the remaining events (nondijet category). When more than two jets are selected, the two jets with the highest pTare chosen
for further analysis.
The systematic uncertainties in the event selection are generally the same as those investigated in Refs.[10,16,17,20]. Among the yield uncertainties, exper-imental systematic uncertainties are evaluated from data for the lepton trigger efficiency and the combination of object reconstruction, identification, and isolation efficiencies. Signal and background uncertainties after the lifetime analysis selection are found to be consistent with the width analysis selection. Most of the signal normalization uncer-tainties are statistical in nature because the signal strength is left unconstrained and because the systematic uncertainties affect only the relative efficiency of 4e, 4μ, and 2e2μ reconstruction. The overall predicted signal cross section is, therefore, not directly used in the analysis, while the theoretical uncertainties in the 4l background remain unchanged compared to Refs. [10,16]. The Zþ X yield uncertainties are estimated to be 20%, 40%, and 25% for the4e, 4μ, and 2e2μ decay channels, respectively, and also remain unchanged compared to Ref.[16].
V. OBSERVABLES
Several observables, such as the four-lepton invariant mass, m4l, or the measured lifetime of each H boson candidate,Δt, are used either as input to likelihood fits or to categorize events in this paper. The full list of observables in each category is shown in TableI, and they are discussed in detail below. The full kinematic information from each event is extracted using the MELA kinematic discrimi-nants, which make use of the correlation between either the two jets and the H boson to identify the production mechanism, or the H→ 4l decay products to identify the decay kinematics. These discriminants use either five, in the case of production, or seven, in the case of decay,
mass and angular input observables ~Ω[35,37]to describe kinematics at LO in QCD. The pTof either the combined H boson and 2 jets system for the production discriminant (Djet)[20]or the H boson itself for the decay discriminants
(Dkin)[2]is not included in the input observables in order to
reduce associated uncertainties.
The discriminant sensitive to the VBF signal topology is calculated as Djet¼ 1 þ PHJJð ~Ω HþJJ; m 4lÞ PVBFð ~ΩHþJJ; m4lÞ −1 ; ð6Þ
wherePVMF andPHJJ are probabilities obtained from the JHUGen matrix elements for the VBF process and gluon
fusion in association with two jets (Hþ 2jets) within the MELA framework [20]. This discriminant is equally efficient in separating VBF from either gg→ H þ 2jets signal or gg or q¯q → 4l þ 2jets background because jet correlations in these processes are distinct from the VBF process.
In the on-shell region, theDjetdiscriminant is one of the
width analysis observables used in the dijet category. The Djetdistribution shown in Fig.2(top) is used to distinguish
gluon fusion, VBF, and VH production mechanisms in this category. The pTof the4l system is used to distinguish the production mechanism of the remaining on-shell events in the nondijet category. In the off-shell region, the require-mentDjet≥ 0.5 is applied instead, keeping nearly half of
the VBF events and less than 4% of all other processes, with only a small dependence on m4l. Events that fail this requirement enter the nondijet category in the off-shell region. The different treatment ofDjetbetween the on-shell
and off-shell regions keeps the observables the same as in the previous width analysis[10].
Uncertainties in modeling the jet distributions affect the separation of events between the two dijet categories but do not affect the combined yield of either signal or background events. For the on-shell dijet category, a 30% normalization uncertainty is taken into account for the gg→ H þ 2jets signal cross section while the uncertainty in the selection of two or more jets from VBF production is 10%. TheDjet
distribution uncertainties other than those for Zþ X are estimated by comparing alternative MC generators and
TABLE I. List of observables, ~x, and categories of events used in the analyses of the H boson lifetime and width. The Djet< 0.5
requirement is defined for Njet≥ 2, but by convention this category also includes events with less than two selected jets, Njet< 2.
Category Mass region Criterion Observables ~x
Lifetime 105.6 < m4l< 140.6 GeV Any Δt Dbkg
Width, on-shell dijet 105.6 < m4l< 140.6 GeV Njet≥ 2 m4l Dkinbkg Djet
Width, on-shell nondijet 105.6 < m4l< 140.6 GeV Njet< 2 m4l Dkinbkg pT
Width, off-shell dijet 220 < m4l< 1600 GeV Djet≥ 0.5 m4l Dgg
Width, off-shell nondijet 220 < m4l< 1600 GeV Djet< 0.5 m4l Dgg
tunings, where smaller effects from uncertainties due to jet energy scale and resolution are also included.
In the off-shell region, the uncertainties in the Djet
distribution imply uncertainties in the categorization requirement Djet> 0.5. To determine the uncertainty in the dijet selection, NLO QCD simulation withPOWHEGis
compared to the two LO generatorsPHANTOMandJHUGen
for the VBF production, all with parton showering simu-lated withPYTHIA. For this comparison, VH production is
omitted from thePHANTOM simulation since no events in
association with electroweak boson production pass the Djet≥ 0.5 requirement. The efficiency of categorization for
VBF-like events is stable within 5%, and the main differ-ence comes from the uncertainty in the additional jet radiation after the hadronization of simulated events at LO or NLO in QCD usingPYTHIA. A similar comparison of
the signal production in gluon fusion is performed between thePOWHEGsimulations at NLO in QCD with and without
theMINLO procedure for multijet simulation, and two LO generators MCFM and GG2VV. With proper matching of the hadronization scale for the LO generators in PYTHIA
[71], a good agreement within 15% is found between all generators, with absolute dijet categorization efficiency of approximately 3%. The m4l dependence of the
categorization efficiency is found to be similar between the different generators.
With the above uncertainties, the contributions of the signal, background, and their interference in the off-shell region for each category are obtained with thePHANTOM
generator for the VBF and associated electroweak boson production, and with the MCFM generator for the gluon fusion production. The dijet categorization efficiency as a function of m4l is reweighted to the POWHEG+MINLO
prediction for gluon fusion signal contribution, and the same reweighting is used in the background and interfer-ence contributions. For the q¯q → ZZ background, the comparison of the NLO QCD simulation with POWHEG
with the two-jet inclusive MadGraph simulation leads to a 25% uncertainty in the dijet categorization. Both dijet categorization and its uncertainty have negligible m4l dependence, and the dijet categorization efficiency is around 0.6%. An uncertainty of 100% is assigned to the categorization of Zþ X events, primarily due to statistical limitations in the data-driven estimate. This uncertainty has a negligible contribution to the results since the contribu-tion of Zþ X is small in the total off-shell expected yield and negligible in the dijet category.
The discriminant sensitive to the gg→ 4l kinematics is calculated as Dkin¼ " 1 þ αP q¯q bkgð ~Ω H→4l; m 4lÞ Pggsigð ~Ω H→4l; m 4lÞ þpffiffiffiβPggintð ~Ω H→4l; m 4lÞ þ βPggbkgð ~Ω H→4l; m 4lÞ #−1 ; ð7Þ
where the denominator contains the sum of the probability contributions from the signal (Pggsig), the background (P
gg bkg),
and their interference (Pggint) to the total gg→ 4l process, and the numerator includes the probability for the q¯q → 4l background process, all calculated either with theJHUGenor
MCFM matrix elements within the MELA framework
[10,16,17]. The two coefficients α and β are tuned differ-ently in the on-shell and off-shell width analysis samples. Signal-background interference effects are negligible in the on-shell region, so the kinematic discriminant is tuned to isolate signal from the dominant background process with Dkin
bkg¼ Dkinðα ¼ 1; β ¼ 0Þ [2,36]. In the off-shell region,
the discriminant is tuned to isolate the full gluon fusion process, including the interference term, for the ratio ΓSM
H =ΓH∼ α ¼ β ¼ 0.1 close to the expected sensitivity
of the analysis. The discriminant is, therefore, labeled as Dgg ¼ Dkinðα ¼ β ¼ 0.1Þ [10].
Apart from the above kinematic discriminants and pT,
the width analysis employs the four-lepton invariant mass m4l as the main observable, which provides signal and background separation in the on-shell region and which is sensitive to theΓH values and anomalous couplings in the
off-shell region. The m4l distributions are illustrated in
Fig. 3 for the on-shell and off-shell regions without any kinematic requirements, Fig. 2 (bottom) for the on-shell region with the requirement Dkin
bkg> 0.5, and Fig. 4 for
the two event categories in the off-shell region, with the requirement Dgg > 2=3 on the nondijet category. The requirements on the kinematic discriminants Dkinbkg or Dgg
suppress the relative contribution of background in the illustration of event distributions. In the lifetime analysis, the m4landDkin
bkgobservables are combined into one, called
Dbkg[14,17,37], in order to reduce the number of
observ-ables. It is constructed by multiplying the matrix element probability ratio in Eq.(7)by the ratio of probabilities for m4l from the nonresonant q¯q → 4l process and the resonant production gg→ H → 4l for the measured mH ¼ 125.6 GeV. The Dbkg distribution in the lifetime
analysis is shown in Fig. 5. To account for the lepton momentum scale and resolution uncertainty in the m4l or Dbkgdistributions, alternative signal distributions are taken
from the variations of both of these contributions. The lifetime analysis makes use of the observable Δt calculated following Eq.(1). The reference point for the H boson production vertex is taken to be the beam spot, which LIMITS ON THE HIGGS BOSON LIFETIME AND WIDTH… PHYSICAL REVIEW D 92, 072010 (2015)
is the pp collision point determined by fitting charged-particle tracks from events in multiple collisions, and the value of Δ~rT is calculated as the displacement from the beam spot to the 4l vertex in the plane transverse to
(GeV) 4 m 110 120 130 140 Events / 2 GeV 0 5 10 Observed H t ggH+t VBF+VH 4 bkg. → gg 4 bkg. → q q Z+X CMS -1 (7 TeV) (8 TeV) + 5.1 fb -1 19.7 fb (GeV) 4 m 400 600 800 Events / 60 GeV 0 50 100 Observed SM H Γ × =10 H Γ -4 10 × =2 Q Λ , f SM H Γ × =10 H Γ =0 VVH μ , -3 10 × =5 Q Λ f π = Q Λ φ , -4 10 × =4.5 Q Λ f 4 total → gg+VV 4 bkg. → q q Z+X CMS -1 (7 TeV) (8 TeV) + 5.1 fb -1 19.7 fb
FIG. 3 (color online). Distributions of the four-lepton invariant mass m4lin the on-shell (top) and off-shell (bottom) regions of the H boson width analysis for all observed and expected events. The points with error bars represent the observed data in both on-shell and off-shell region distributions. The histo-grams for the on-shell region represent the expected contribu-tions from the SM backgrounds and the H boson signal with the contribution from the VBF and VH production shown separately. The filled histograms for the off-shell region represent the expected contributions from the SM backgrounds and H boson signal, combining gluon fusion, VBF, and VH processes. Alternative H boson width and coupling scenarios are shown as open histograms with the assumption ϕΛQ¼ 0 unless specified otherwise, and the overflow bin includes events up to m4l¼ 1600 GeV. jet D 0 0.2 0.4 0.6 0.8 1 Events / 0.04 0 2 4 6 Observed H t ggH+t VBF+VH 4 bkg. → gg 4 bkg. → q q Z+X CMS -1 (7 TeV) (8 TeV) + 5.1 fb -1 19.7 fb (GeV) 4 m 110 120 130 140 Events / 2 GeV 0 5 10 Observed H t ggH+t VBF+VH 4 bkg. → gg 4 bkg. → q q Z+X CMS -1 (7 TeV) (8 TeV) + 5.1 fb -1 19.7 fb
FIG. 2 (color online). Distributions ofDjet(top) and the
four-lepton invariant mass m4l(bottom) in the on-shell region of the H boson width analysis. TheDjet distributions show events in the
dijet category with a requirement 120 < m4l< 130 GeV. The m4l distributions combine the nondijet and dijet categories, the former with an additional requirementDkinbkg> 0.5 to suppress
the dominant q¯q → 4l background. The points with error bars represent the observed data, and the histograms represent the expected contributions from the SM backgrounds and the H boson signal. The contribution from the VBF and VH production is shown separately.
the beam axis. An alternative calculation of Δt has also been considered using the primary vertex of each event instead of the beam spot, but the different associated particles in the H boson production and their multiplicity
(GeV) 4 m 400 600 800 Events / 60 GeV 0 5 10 Observed SM H Γ × =10 H Γ -4 10 × =2 Q Λ , f SM H Γ × =10 H Γ =0 VVH μ , -3 10 × =5 Q Λ f π = Q Λ φ , -4 10 × =4.5 Q Λ f 4 total → gg+VV 4 bkg. → q q Z+X CMS 19.7 fb-1 (8 TeV) + 5.1 fb-1 (7 TeV) (GeV) 4 m 400 600 800 Events / 60 GeV 0 1 2 3 4 5 Observed SM H Γ × =10 H Γ -4 10 × =2 Q Λ , f SM H Γ × =10 H Γ =0 VVH μ , -3 10 × =5 Q Λ f π = Q Λ φ , -4 10 × =4.5 Q Λ f 4 total → gg+VV 4 bkg. → q q Z+X CMS 19.7 fb-1 (8 TeV) + 5.1 fb-1 (7 TeV)
FIG. 4 (color online). Distribution of the four-lepton invariant mass m4lin the off-shell region in the nondijet (top) and dijet (bottom) categories. A requirementDgg> 2=3 is applied in the
nondijet category to suppress the dominant q¯q → 4l back-ground. The points with error bars represent the observed data, and the filled histograms represent the expected contributions from the SM backgrounds and H boson signal, combining gluon fusion, VBF, and VH processes. Alternative H boson width and coupling scenarios are shown as open histograms. The overflow bins include events up to m4l¼ 1600 GeV, and ϕΛQ¼ 0 is assumed where it is unspecified.
bkg D 0 0.2 0.4 0.6 0.8 1 Events / 0.05 0 5 10 15 20 Observed SM signal 4 bkg. → gg 4 bkg. → q q Z+X CMS -1 (7 TeV) (8 TeV) + 5.1 fb -1 19.7 fb m) μ t ( Δ c -500 0 500 mμ Events / 40 0 2 4 6 8 Observed SM signal m μ =100 H τ c 4 bkg. → gg 4 bkg. → q q Z+X CMS 19.7 fb-1 (8 TeV) + 5.1 fb-1 (7 TeV)
FIG. 5 (color online). Distributions of Dbkg (top) and cΔt
(bottom) in the lifetime analysis withDbkg> 0.5 required for
the latter to suppress the background. The points with error bars represent the observed data, and the filled histograms stacked on top of each other represent the expected contri-butions from the SM backgrounds. Stacked on the total background contribution, the open histograms show the combination of all production mechanisms expected in the SM for the H boson signal with either the SM lifetime or cτH¼ 100 μm. Each signal contribution in the different
open histograms are the same as the total number of events expected from the combination of all production mechanisms in the SM. All signal distributions are shown with the total number of events expected in the SM. The first and last bins of the cΔt distributions include all events beyond jcΔtj > 500 μm.
would introduce additional model dependence in the primary vertex resolution.
TheΔt value is non-negative and follows the exponen-tial decay distribution if it is known perfectly for each event. However, resolution effects arising mostly from limited precision of the Δ~rT measurement allow negative
Δt values. This feature allows for an effective self-calibration of the resolution from the data. Symmetric broadening of the Δt distribution indicates resolution effects while positive skew indicates sizable signal life-time. Figure 5 displays the Δt distributions. The reso-lution in Δt also depends on the pT spectrum of the
produced H boson, which differs among the production mechanisms, and this dependence is accounted for in the fit procedure as described in detail in Sec. VI. The distributions of Δt and pT are shown in Figs. 5 and 6, respectively. Since the discriminant Dbkg is optimal for signal separation in the on-shell region, a requirement Dbkg> 0.5 is applied to reduce the background when
showing these distributions.
Uncertainties in theΔt distribution for the signal and the prompt background are obtained from a comparison of the
expected and observed distributions in the m4l sidebands, 70 < m4l< 105.6 GeV and 170 < m4l< 800 GeV.
These uncertainties obtained from this comparison corre-spond to varying the Δt resolution by þ17= − 15%, þ14= − 12%, and þ20= − 17% for the 4e, 4μ, and 2e2μ final states, respectively. The Zþ X parametrization is obtained from the control region in the analysis mass range 105.6 < m4l< 140.6 GeV, and its alternative
parametri-zation obtained from the control region events in the mass range140.6 < m4l< 170 GeV reflects the uncertainties in the data-driven estimate. A cross-check of the Δt distri-butions is also performed with the 3l control samples enriched in WZ prompt decay, and the distributions are found to be consistent with simulation.
VI. CONSTRAINTS ON THE LIFETIME The H boson lifetime analysis is based on two observ-ables ~x ¼ ðΔt; DbkgÞ, which allow the measurement of the
average signal lifetimeτH and the discrimination of the H
boson signal from background using a simultaneous like-lihood fit. The extended likelike-lihood function is defined for Nev candidate events as L ¼ exp −nsig− X k nðkÞbkg Y Nev i × nsigPsigð~xi; ~ξÞ þ X k nðkÞbkgPðkÞbkgð~xi; ~ζÞ ; ð8Þ
where nsig is the number of signal events and nkbkg is the number of background events of type k (gg→ 4l, q¯q → 4l, Z þ X). The probability density functions, Psig for signal and Pkbkg for each background process k, are described as histograms (templates). The likelihood para-metrization is constructed independently in each of the4e, 4μ, or 2e2μ final states, and for 7 and 8 TeV pp collision energy. The parameters ~ξ for the signal and ~ζ for the background processes include parametrization uncertain-ties, and ~ξ also includes τHas the parameter of interest. The likelihood in Eq. (8) is maximized with respect to the parameters nsig, nkbkg, ~ξ and ~ζ, which constitute the nuisance
parameters and the parameter of interest. The nuisance parameters are either constrained within the associated uncertainties or left unconstrained in the fit.
The kinematics of the four-lepton decay, affectingDbkg,
and the four-lepton vertex position and resolution, affecting Δt, are found to be independent. Therefore, the two-dimensional probability distributions of PðΔt; DbkgÞ are constructed as the product of two one-dimensional distri-butions. In the case of the signal probability, the Δt templates are conditional on the parameter of interestτH. The signal Δt parametrization is obtained for the range 0 ≤ cτH ≤ 1000 μm by reweighting the simulation (GeV) T p 0 50 100 150 200 Events / 10 GeV 0 5 10 Observed SM signal VBF signal H signal t t 4 bkg. → gg 4 bkg. → q q Z+X CMS 19.7 fb-1 (8 TeV) + 5.1 fb-1 (7 TeV)
FIG. 6 (color online). Distributions of the four-lepton pTwith
the selection used in the lifetime analysis and the requirement Dbkg> 0.5 to suppress the backgrounds. The points with error
bars represent the observed data, and the filled histograms stacked on top of each other represent the expected contributions from the SM backgrounds. Stacked on the total background contribution, the open histograms show the H boson signal either with the combination of all production mechanisms expected in the SM, or for the VBF or t¯tH production mechanisms. Each signal contribution in the different open histograms is normalized to the total number of events expected from the combination of all production mechanisms in the SM. The overflow bin includes all events beyond pT> 200 GeV.
available for the gluon fusion process at cτH ¼ 0, 100, 500,
and 1000 μm to cτH values in steps of 10 μm and
interpolating linearly for any intermediate value.
TheΔt parametrization for all SM H boson production mechanisms (gluon fusion, VBF, WH, ZH, and t¯tH) is obtained by reweighting gluon fusion production events as a function of pT at each of the τH values. This procedure
reproduces Δt resolution effects predicted from the simu-lation for prompt signal (i.e.τH ¼ 0) and is, therefore, valid
for nonzero lifetime. As shown in Fig.6, the gluon fusion production mechanism has the softest pT spectrum while t¯tH production yields the hardest pT, and the distribution of Δt is thus wider in gluon fusion and narrower in t¯tH production, with other production mechanisms in between. Gluon fusion production and t¯tH distributions, with their respective yields scaled to the total SM production cross section, are therefore taken as the two extreme variations while the nominalΔt distribution is parametrized with the SM combination of the different production mechanisms. TheΔt distribution used in the likelihood is varied from the nominal prediction between these two extremes with a continuous production parameter included in ~ξ in Eq.(8). Any other production mechanism or a mixture can be described with this parametrization, and the values of the production parameter corresponding to the pTspectrum of
either pure VBF, WH, ZH, or t¯tH mechanisms are excluded at more than 95% C.L. from a fit to data. This information is consistent with the observed pT spectrum
in Fig. 6.
While the Δt and Dbkg parametrizations are obtained for the SM couplings in the H→ ZZ → 4l decay, and for pT spectra as in SM-like production mechanisms
(gluon fusion, VBF, WH, ZH, and t¯tH), the analysis has little dependence on anomalous couplings in either the production or the decay of the H boson. It has already been established [17] that the kinematics of the H→ 4l decay are consistent with the kinematics of the SM H boson decay and inconsistent with a wide range of exotic models. The Δt and Dbkg distributions have little
varia-tion within the allowed range of exotic couplings in the H → 4l decay. The expected τH constraint remains stable
within 10% when the simulation for those exotic models is tested instead of the simulation with SM couplings. Anomalous couplings in production are found to have a substantial effect on the pT spectrum, typically making
the spectrum harder in the VBF, WH, ZH, and t¯tH production mechanisms. Extreme variations in the pT spectrum, however, are already excluded by the data, and pT variations allowed by the data are reflected in the Δt parametrization with the parameter describing the pro-duction mechanisms.
Figure7shows the likelihood distribution as a function of cτH. The allowed 68% and 95% C.L. intervals are
defined using the respective profile likelihood function values −2 lnðL=LmaxÞ ¼ 1.00 and 3.84 for which exact
coverage is expected in the asymptotic limit [72]. The approximate coverage has been tested with the generated samples at different cτHvalues, and the quoted results have
been found to be conservative. The observed (expected) average lifetime is cτH ¼ 2þ25−2 ð0þ24−0 Þ μm (τH ¼ 10þ80−10 fs for the observation andτH ¼ 0þ80−0 fs for the expectation),
and the allowed region at the 95% C.L. is cτH < 57ð56Þ μm (τH < 190 fs for both the observation and
the expectation). The observed number of signal events remains consistent with Ref.[16]. The observed (expected) upper limit on the average lifetime at 95% C.L. corresponds through Eq.(2) to the lower limit on the H boson width ΓH > 3.5 × 10−9 MeV (ΓH > 3.6 × 10−9 MeV) regardless
of the value of fΛQ.
VII. CONSTRAINTS ON THE WIDTH The H boson width ΓH and the effective fraction fΛQ for the ΛQ anomalous coupling are measured in an unbinned maximum likelihood fit of a signal-plus-background model following Eq. (8). In addition to the event categories already defined in the lifetime analysis for the final states and pp collision energy, events are also split into dijet and nondijet categories, and into on-shell and off-on-shell regions. In the on-on-shell region, a three-dimensional distribution of ~x ¼ ðm4l; Dkinbkg; pTorDjetÞ is
analyzed, following the methodology described in Ref. [16]. In the off-shell region, a two-dimensional distribution ~x ¼ ðm4l; DggÞ is analyzed following the
methodology described in Ref.[10]with the events split into the two dijet categories defined in TableI.
m) μ ( H τ c 0 20 40 60 80 100 120 140 160 180 200 lnLΔ -2 0 2 4 6 8 10 12 14 16 18 Observed Expected SM CMS 19.7 fb-1 (8 TeV) + 5.1 fb-1 (7 TeV) 68% CL 95% CL
FIG. 7. Observed (solid) and expected (dashed) distributions of −2 lnðL=LmaxÞ as a function of the H boson average lifetime cτH.
The probability distribution functions are built using the full detector simulation or data control regions and are defined for both the signal (Psig) and the background (Pbkg) contributions as well as their interference (Pint), as a function of the
observables ~x discussed above. Several production mechanisms such as gluon fusion (gg), VBF, WH and ZH (VH) are considered for the signal. The total probability distribution function for the off-shell region is written as
Poff-shell tot ð~x; ΓH; fΛQÞ ¼ 2 6 4μggHΓΓH 0P gg sigð~x; fΛQÞ þ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi μggHΓΓH 0 s Pggintð~x; fΛQÞ þ P gg bkgð~xÞ 3 7 5 þ 2 6 4μVVHΓH Γ0P VV sigð~x; fΛQÞ þ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi μVVHΓH Γ0 s PVV intð~x; fΛQÞ þ PVVbkgð~xÞ 3 7 5 þ Pq¯qbkgð~xÞ þ PZXbkgð~xÞ; ð9Þ
where Γ0 is a reference value used in simulation and VV stands for a combination of VBF and associated electro-weak boson production taken together. Under the assumption ϕΛQ¼ 0 or π, any contribution to the HVV scattering amplitude in Eq. (4) from the a1 term is proportional to pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1 − fΛQ while that from the ΛQ term
is proportional topffiffiffiffiffiffiffiffifΛQcosðϕΛQÞ. The dependence on fΛQ in Eq.(9) can thus be parametrized with the factor
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 − fΛQ p −pffiffiffiffiffiffiffiffifΛQcosðϕΛQÞm 2 4l m2 H N ; ð10Þ
where the power N depends on the power of the HVV couplings. The couplings appear twice in the VBF and VH cases, in both production and decay, so the power of the factor is twice as large. Thus, for gluon fusion, N¼ 1 for the interference component (Pggint) and N¼ 2 for the signal (Pggsig); for VBF and VH, N¼ 2 (PVVint) and 4 (PVVsig), respectively. Both HZZ and HWW couplings contribute to the VBF and VH production couplings, and this analysis assumes the same ΛQ would contribute to the HZZ and
HWW couplings in Eq.(4). The effective fraction fΛQ is therefore the same for the HZZ and HWW amplitudes.
In the on-shell region, the parametrization includes the small contribution of the t¯tH production mechanism, which is related to the gluon fusion production. The total probability distribution function for the on-shell region is
Pon-shell
tot ð~xÞ ¼ μggHPggþt¯tHsig ð~xÞ þ μVVHPVVsigð~xÞ
þ Pq¯qbkgð~xÞ þ P gg
bkgð~xÞ þ PZXbkgð~xÞ: ð11Þ
The normalization of the signal and background distribu-tions is incorporated in the probability funcdistribu-tions P in Eqs. (9) and (11), but the overall signal yield is left unconstrained with the independent signal strength param-eters μggH and μVVH, corresponding to the H production mechanisms through coupling to either fermions or weak vector bosons, respectively. The observedμggH andμVVH
values are found to be consistent with those obtained in Refs.[10,16].
The allowed 68% and 95% C.L. intervals are defined using the profile likelihood function values −2 lnðL=LmaxÞ ¼ 2.30 and 5.99, respectively, for the
two-parameter constraints presented, and−2 lnðL=LmaxÞ ¼
1.00 and 3.84, respectively, for the one-parameter con-straints. Exact coverage is expected in the asymptotic limit [72], and the approximate coverage has been tested at several different parameter values with the quoted results having been found to be conservative. The observed distribution of the likelihood as a two-parameter function of ΓH and fΛQcosϕΛQ, with ϕΛQ¼ 0 or π, is shown in Fig. 8. Also shown is the one-parameter, conditional likelihood scan of fΛQcosϕΛQ for a given ΓH, where the−2 lnðL=LmaxÞ distribution is shown for Lmaxadjusted
according to the most likely value of fΛQcosϕΛQ at the given value ofΓH. The observed and expected likelihood distributions as a function ofΓH are shown in Fig.9, where
fΛQis either constrained to zero or left unconstrained. The observed (expected) central values with 68% C.L. uncer-tainties areΓH ¼ 2þ9−2ð4þ17−4 Þ MeV with fΛQ¼ 0, and ΓH ¼
2þ15
−2 ð4þ30−4 Þ MeV with fΛQ unconstrained andϕΛQ¼ 0 or
π. The observed (expected) constraints at 95% C.L. are ΓH < 26ð41Þ MeV with fΛQ ¼ 0, and ΓH < 46ð73Þ MeV
with fΛQunconstrained andϕΛQ¼ 0 or π. These observed (expected) upper limits on the H boson width at 95% C.L. correspond through Eq.(2) to the lower limits on the H boson average lifetime τH > 2.5 × 10−8ð1.6 × 10−8Þ fs
with fΛQ¼ 0 and τH > 1.4 × 10−8ð9 × 10−9Þ fs with fΛQ unconstrained andϕΛQ¼ 0 or π.
The result with the constraint fΛQ¼ 0 is consistent with the earlier one from the H→ ZZ → 4l channel[10]. It can be reinterpreted as an off-shell signal strength with the change of parametersμoff-shell
vvH ¼ μvvHΓH=ΓSMH , provided the
signal strengthμvvHfor the on-shell region is uncorrelated
with the signal strengthμoff-shell
vvH for the off-shell region in
the likelihood scan. The observed (expected) central values and the 68% C.L. uncertainties of ΓH with the fΛQ¼ 0
constraint correspond to μoff-shellggH ¼ 0.5þ2.2−0.5ð1.0þ5.1−1.0Þ and μoff-shell
VVH ¼ 0.4þ10.5−0.4 ð1.0þ20.6−1.0 Þ, and the observed (expected)
constraints at 95% C.L. become μoff-shell
ggH < 6.2ð9.3Þ and
μoff-shell
VVH < 31.3ð44.4Þ. There is no constraint on the ratio
μoff-shell
VVH =μoff-shellggH at 68% C.L.. The ΓH limits with fΛQ
unconstrained are weaker because a small nonzero value fΛQ∼ 2 × 10−4 leads to destructive interference between
the a1 and ΛQ terms in Eq. (4) when ϕΛQ¼ 0. This
interference reduces the expected signal yield at these parameter values, thereby reducing the exclusion power for ΓH > ΓSMH . This effect is also illustrated in Fig.4.
No constraint on fΛQcan be obtained in the limitΓH → 0
because, as displayed in Fig.8, the number of expected off-shell events vanishes. The constraints on fΛQcosϕΛQgiven
particularΓH values become tighter for increasingΓH. The
limits on fΛQcosϕΛQ with the assumption ΓH ¼ ΓSMH are
presented in Fig. 9. The observed (expected) value is fΛQcosϕΛQ¼ 0þ1.0−0.4ð0þ1.1−0.4Þ × 10−3, and the allowed region at 95% C.L. is½−2.4; 3.8 × 10−3ð½−3.6; 4.4 × 10−3Þ.
VIII. CONCLUSIONS
Constraints on the lifetime and the width of the H boson are obtained from H→ ZZ → 4l events using the data
(MeV) H Γ 0 20 40 60 80 100 120 lnLΔ -2 0 5 10 15 20 ) unconstrained Q Λ φ cos( Q Λ Observed, f ) unconstrained Q Λ φ cos( Q Λ Expected, f =0 Q Λ Observed, f =0 Q Λ Expected, f CMS -1 (7 TeV) (8 TeV) + 5.1 fb -1 19.7 fb 68% CL 95% CL ) Q Λ φ cos( Q Λ f -0.01 -0.005 0 0.005 0.01 lnLΔ -2 5 10 15 H SM Γ = H Γ Observed, H SM Γ = H Γ Expected, CMS 19.7 fb-1 (8 TeV) + 5.1 fb-1 (7 TeV) 68% CL 95% CL
FIG. 9 (color online). Observed (solid) and expected (dashed) distributions of −2 lnðL=LmaxÞ as a function of ΓH (top) and
fΛQcosϕΛQ (bottom). On the top panel, the fΛQ value is either constrained to zero (blue) or left unconstrained (black, weaker limit), whileΓH¼ ΓSMH andϕΛQ¼ 0 or π are assumed on the bottom.
0 10 20 30 40 50 (MeV) H Γ 0 20 40 60 80 100 120 ) QΛ φ cos( QΛ f -0.01 -0.005 0 0.005 0.01 lnL=5.99 Δ -2 lnL=2.3 Δ -2 Best fit SM CMS -1 (7 TeV) (8 TeV) + 5.1 fb -1 19.7 fb ln LΔ -2 0 5 10 15 20 25 30 35 40 (MeV) H Γ 0 20 40 60 80 100 120 ) QΛ φ cos( QΛ f -0.01 -0.005 0 0.005 0.01 lnL=3.84 Δ -2 lnL=1 Δ -2 SM Δ -2 lnL=1 Δ -2 CMS -1 (7 TeV) (8 TeV) + 5.1 fb -1 19.7 fb ln LΔ -2
FIG. 8 (color online). Observed distribution of−2 lnðL=LmaxÞ
as a function ofΓHand fΛQcosϕΛQwith the assumptionϕΛQ¼ 0
orπ (top panel). The bottom panel shows the observed conditional likelihood scan as a function of fΛQcosϕΛQfor a givenΓH. The
likelihood contours are shown for the two-parameter 68% and 95% CLs (top) and for the one-parameter 68% and 95% CLs
(bottom). The black curve with white dots on the bottom panel shows the fΛQcosϕΛQminima at eachΓHvalue.
recorded by the CMS experiment during the LHC run 1. The measurement of the H boson lifetime is derived from its flight distance in the CMS detector with the upper bound τH < 190 fs at the 95% C.L., corresponding to a lower
bound on the widthΓH > 3.5 × 10−9 MeV. The
measure-ment of the width is obtained from an off-shell production technique, generalized to include additional anomalous couplings of the H boson to two electroweak bosons. This measurement provides a joint constraint on the H boson width and a parameter that quantifies an anomalous coupling contribution through an on-shell cross-section fraction fΛQ. The observed limit on the H boson width is ΓH < 46 MeV at the 95% C.L. with fΛQleft unconstrained
while it isΓH < 26 MeV at the 95% C.L. for fΛQ¼ 0. The
constraint fΛQ< 3.8 × 10−3 at the 95% C.L. is obtained assuming the H boson width expected in the SM, and the fΛQ constraints given any other width value are also presented. TableIIsummarizes the width and correspond-ing lifetime limits, and TableIIIsummarizes the limits on fΛQ under the different ϕΛQ scenarios that can be inter-preted from this analysis, and provides the corresponding limits on p Λffiffiffiffiffia1 Q.
ACKNOWLEDGMENTS
We thank Markus Schulze for optimizing the JHUGen
Monte Carlo simulation program and matrix element library for this analysis. We congratulate our colleagues in the CERN accelerator departments for the excellent performance of the LHC and thank the technical and administrative staffs at CERN and at other CMS institutes for their contributions to the success of the CMS effort. In
addition, we gratefully acknowledge the computing centers and personnel of the Worldwide LHC Computing Grid for delivering so effectively the computing infrastructure essential to our analyses. Finally, we acknowledge the enduring support for the construction and operation of the LHC and the CMS detector provided by the following funding agencies: the Austrian Federal Ministry of Science, Research and Economy and the Austrian Science Fund; the Belgian Fonds de la Recherche Scientifique, and Fonds voor Wetenschappelijk Onderzoek; the Brazilian Funding Agencies (CNPq, CAPES, FAPERJ, and FAPESP); the Bulgarian Ministry of Education and Science; CERN; the Chinese Academy of Sciences, Ministry of Science and Technology, and National Natural Science Foundation of China; the Colombian Funding Agency (COLCIENCIAS); the Croatian Ministry of Science, Education and Sport, and the Croatian Science Foundation; the Research Promotion Foundation, Cyprus; the Ministry of Education and Research, Estonian Research Council via IUT23-4 and IUT23-6 and European Regional Development Fund, Estonia; the Academy of Finland, Finnish Ministry of Education and Culture, and Helsinki Institute of Physics; the Institut National de Physique Nucléaire et de Physique des Particules/CNRS, and Commissariat à l’Énergie Atomique et aux Énergies Alternatives/CEA, France; the Bundesministerium für Bildung und Forschung, Deutsche Forschungsgemeinschaft, and Helmholtz-Gemeinschaft Deutscher Forschungszentren, Germany; the General Secretariat for Research and Technology, Greece; the National Scientific Research Foundation, and National Innovation Office, Hungary; the Department of Atomic Energy and the Department of Science and Technology, TABLE II. Observed and expected allowed intervals at the 95% C.L. on the H boson average lifetimeτH and widthΓHobtained
combining the width and lifetime analyses. The constraints are separated into the two conditions used in the width measurement, with either the constraint fΛQ¼ 0, or fΛQleft unconstrained andϕΛQ ¼ 0 or π. The upper (lower) limits on H boson average lifetime τHare
related to the lower (upper) limits on H boson widthΓH through Eq.(2).
fΛQ¼ 0 fΛQ unconstrained,ϕΛQ¼ 0 or π
Parameter Observed Expected Observed Expected
τH (fs) ½2.5 × 10−8; 190 ½1.6 × 10−8; 190 ½1.4 × 10−8; 190 ½9 × 10−9; 190
ΓH (MeV) ½3.5 × 10−9; 26 ½3.6 × 10−9; 41 ½3.5 × 10−9; 46 ½3.6 × 10−9; 73
TABLE III. Observed and expected allowed intervals at the 95% C.L. on the fΛQ on-shell effective cross-section fraction and its interpretation in terms of the anomalous coupling parameterΛQassumingΓH¼ ΓSM
H . Results are presented assuming eitherϕΛQ¼ 0 or
ϕΛQ¼ π. The allowed intervals on fΛQare also translated to the equivalent quantityp Λffiffiffiffiffia1 Qthrough Eq.(5), where the coefficient a1is
allowed to be different from its SM value a1¼ 2.
ϕΛQ¼ 0 ϕΛQ¼ π
Parameter Observed Expected Observed Expected
fΛQ < 3.8 × 10−3 < 4.4 × 10−3 < 2.4 × 10−3 < 3.6 × 10−3
ffiffiffiffiffi a1
p ΛQ(GeV) > 500 > 490 > 570 > 510
India; the Institute for Studies in Theoretical Physics and Mathematics, Iran; the Science Foundation, Ireland; the Istituto Nazionale di Fisica Nucleare, Italy; the Ministry of Science, ICT and Future Planning, and National Research Foundation (NRF), Republic of Korea; the Lithuanian Academy of Sciences; the Ministry of Education, and University of Malaya (Malaysia); the Mexican funding agencies (CINVESTAV, CONACYT, SEP, and UASLP-FAI); the Ministry of Business, Innovation and Employment, New Zealand; the Pakistan Atomic Energy Commission; the Ministry of Science and Higher Education and the National Science Centre, Poland; the Fundação para a Ciência e a Tecnologia, Portugal; JINR, Dubna; the Ministry of Education and Science of the Russian Federation, the Federal Agency of Atomic Energy of the Russian Federation, Russian Academy of Sciences, and the Russian Foundation for Basic Research; the Ministry of Education, Science and Technological Development of Serbia; the Secretaría de Estado de Investigación, Desarrollo e Innovación and Programa Consolider-Ingenio 2010, Spain; the Swiss Funding Agencies (ETH Board, ETH Zurich, PSI, SNF, UniZH, Canton Zurich, and SER); the Ministry of Science and Technology, Taipei; the Thailand Center of Excellence in Physics, the Institute for the Promotion of Teaching Science and Technology of Thailand, Special Task Force for Activating Research and the National Science and Technology Development Agency
of Thailand; the Scientific and Technical Research Council of Turkey, and Turkish Atomic Energy Authority; the National Academy of Sciences of Ukraine, and State Fund for Fundamental Researches, Ukraine; the Science and Technology Facilities Council, UK; the U.S. Department of Energy, and the U.S. National Science Foundation. Individuals have received support from the Marie Curie program and the European Research Council and EPLANET (European Union); the Leventis Foundation; the A. P. Sloan Foundation; the Alexander von Humboldt Foundation; the Belgian Federal Science Policy Office; the Fonds pour la Formation à la Recherche dans l’Industrie et dans l’Agriculture (FRIA-Belgium); the Agentschap voor Innovatie door Wetenschap en Technologie (IWT-Belgium); the Ministry of Education, Youth and Sports (MEYS) of the Czech Republic; the Council of Science and Industrial Research, India; the HOMING PLUS program of the Foundation for Polish Science, cofinanced by the European Union, Regional Development Fund; the Compagnia di San Paolo (Torino); the Consorzio per la Fisica (Trieste); MIUR project 20108T4XTM (Italy); the Thalis and Aristeia programs cofinanced by EU-ESF and the Greek NSRF; the National Priorities Research Program by Qatar National Research Fund; the Rachadapisek Sompot Fund for Postdoctoral Fellowship, Chulalongkorn University (Thailand); and the Welch Foundation.
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